The particle P moves along the x-axis such that its velocity, $v$ m/s, at time $t$ seconds is given by $v=\cos t^2$. Given that P is at the origin O at time $t=0$, what is the time at which the total distance travelled by P is 1 m?
To find the answer, I know I must find t in the following equation: $$\int_0^t|\cos u^2|du=1$$
However, I do not know how to input this in a calculator (I have TI-84 Plus) or use any other method to solve it.
The comment of benguin may get around the problem fast. But here is an algorithmic approach which should probably work on your TI-84 (I don't know its language of programmation, but it looks as if it is programmable, $f(u)=abs(cos(u^2))$ is your function that should be integrated)
t=0; I=0;
dt=0.001;
while $I<1$ do
$\mbox{ }$ I = I + (f(t) + f(t+dt)) * dt/2;
$\mbox{ }$ t=t+dt;
end;
output t
The result is (probably) in the interval $[t-dt,t]$. The algorithm calculates numerically the integral until the value 1 is exceeded. For more precision the 'trapez' method may be replaced by a Simpson formula. However, if you haven't learned about numeric integration then the idea is probably that you should use the 'black box' method suggested by benguin.